Correlations, causes and heuristics in surveys of life satisfaction

C R A I G R. F O X A N D D A N I E L K A H N E M A N
CORRELATIONS,
CAUSES AND HEURISTICS
IN
SURVEYS OF LIFE SATISFACTION
(Accepted 14 January, 1991)
ABSTRACT. Satisfaction with life domains is more highly correlated with interpersonal
than with intrapersonal comparisons (Emmons and Diener, 1985). The hypothesis of
the present studies is that the high correlations reflect inferences of social comparison
from global satisfaction. Paradoxically, such inferences are most likely in private
domains (love life, friends), where social information is scarce and relatively unimportant as a determinant of satisfaction. Study I replicates the Emmons-Diener findings,
but also finds that subjects judge recent changes more important than social standing as
a determinant of life satisfaction, especially in private domains. Study 1I examines an
order effect in judgments of satisfaction. As hypothesized the correlation between social
comparison and global satisfaction is higher (in private domains only) when global
satisfaction is judged first than when the order of judgment is reversed.
The main goal of the study of subjective well-being is to understand the
causes of human happiness and misery. This goal has often been sought
through the correlational analysis of people's evaluations of various
aspects of their lives. The correlational analysis accepts the ratings of
particular life domains as valid indications of satisfaction in these
domains, and assumes that the overall evaluation of happiness or wellbeing is based on these constituent assessments. Both assumptions are
called into question by an alternative approach to judgments of wellbeing (e.g., the "judgment model" of Schwarz and Strack, 1991), which
Diener (1989) has labeled "constructionist."
The central idea of the constructionist approach is that answers to
well-being surveys are not read-outs of stable internal states, but instead
represent ad hoc constructions, evoked by the specific question in its
particular context. Responses are understood as outcomes of a cognitive process which involves interpretation, memory search, evaluation,
and editing (see also Tourangeau, 1984; Hippler et aL, 1987). An
important implication of this view is that correlations between judgments of different variables may reflect the heuristic use of one
judgment to make another, rather than a causal effect of one of the
Social Indicators Research 27:221--234, 1992.
9 1992 Kluwer Academic Publishers. Printed in the Netherlands.
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CRAIG R. FOX A N D DANIEL KAHNEMAN
judged variables on the other. The present report is concerned with a
particular case of this ambiguity in the interpretation of correlational
results.
A basic finding of well-being research is that objective circumstances
and actual achievements are poor predictors of satisfaction with financial status, grades, physical condition, and other life domains (Argyle,
1987). Instead, satisfaction is mainly determined by an explicit or
implicit comparison of the current state to some reference norm or
standard. One tradition of research has emphasized the role of social
comparisons in determining feelings of satisfaction or relative deprivation (e.g., Crosby, 1982; Festinger, 1954). Another tradition has
emphasized comparisons to an adaptation level, which is mainly
determined by the individual's personal history (e.g., Brickman and
Campbell, 1971; Helson, 1964).
The starting point of our inquiry is a seemingly straightforward
question: What is the relative importance of social comparisons and
individual history in the evaluation of satisfaction with particular
domains of life? Evidence on the relative importance of interpersonal
and intrapersonal comparisons is scant and inconsistent. A large study
of financial well-being conducted by Dutch economists (van de Stadt
et al., 1985) concluded that comparisons to the individual's past have
substantially greater weight than comparisons to reference groups in
determining satisfaction. However, a study by Emmons and Diener
(1985) favors the opposite conclusion. The present note discusses the
findings of the Emmons-Diener study.m
Emmons and Diener (1985) presented 149 students with detailed
questions about their satisfaction with 11 domains of their lives. The
criterion variable for each domain was a satisfaction rating, worded as
follows: "Please rate below how satisfied you are with each area of your
life presently." The analysis focused on the prediction of this variable
from other measures obtained in the same questionnaire, including selfreports of social (interpersonal) comparisons and recent change (intrapersonal comparisons).
Table I presents a subset of the data reported in Table HI of the
Emmons-Diener (1985) study. The salient finding is that for most
domains social comparison ratings predict satisfaction much better than
do ratings of recent change. The first-order correlations (not shown
CAUSES
AND HEURISTICS
223
TABLE I
Standardized beta weights predicting satisfaction f r o m E m m o n s and Diener (1985)
Domain
Social
comparison
Recent
change
Friends
Love life
Grades
Housing
Physical attractiveness
Standard of living
Family
Recreation
Religion
Courses
Future career
0.46 b
0.57 a
0.25b
0.15 a
0.39 b
0.27 b
0.29 b
0.34b
0.25 b
0.07
0.31 b
0.14 a
0.14 b
0.19 b
0.00
0.03
0.06
0.08
0.12
0.06
0.240
0.18b
S u m across d o m a i n s
0.49 b
0.03
a p < 0.05
b p < 0.01
N = 149
here) support the same conclusion: over the 11 domains, the average
correlation of satisfaction with a measure of social comparison was
0.64, whereas the average correlation of satisfaction with a measure of
recent change was only 0.30. These results suggest that social comparisons dominate intrapersonal contrasts in determining satisfaction.
Emmons and Diener appreciated the need for caution in interpreting
these correlational findings; they concluded their brief discussion of the
results with the following observation: "One topic for future research is
to uncover the direction of the influence between social comparison
and subjective well-being. It is plausible that in some cases a feeling of
well-being leads to high social comparison estimates; in other cases the
influence may occur in the other direction, and frequently the influence
may be bidirectional." (p. 163) As is often the case, however, this note
of caution was dropped in secondary references to the study, which
portray social comparison as the strongest predictor -- and by implication the most important cause of satisfaction (Diener, 1984: Smith
et al., 1989).
Predicting and explaining global variables by their more specific constituents is intuitively appealing. In the context of well-being research,
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CRAIG R. FOX AND DANIEL KAHNEMAN
this intuition suggests that global satisfaction with life should be
explained by satisfaction with various life domains, and that satisfaction
with each domain should be explained in turn by more specific
measures, such as evaluations of inter- and intrapersonal comparisons.
However, the constructionist perspective suggests caution. In this
approach, difficult judgments are made by using the most accessible
relevant information and by relying heuristically on simpler judgments
or on other accessible cues such as current mood (Schwarz and Clore,
1983). Global judgments will therefore be derived from more specific
constituents mainly to the extent that the latter are more accessible or
easily judged. Conversely, if global satisfaction with a particular domain
is more easily judged than social comparison, the global judgment could
serve as a heuristic for the specific. It is plausible to assume, for
example, that most people are keenly aware of their own happiness or
misery in the domain of love, but relatively ignorant of the love lives of
others. In the absence of more direct information about other people,
one's own satisfaction can be used to guess how one compares to
others. It is such social ignorance that permits many lovers to describe
themselves as "the happiest person in the world".
The present account suggests the perverse hypothesis that the correlation between judgments of social comparison and of global satisfaction may be especially high in domains where people know little about
others. In such cases, of course, subjective social comparison is an ad
hoc construction that plays little or no part in the causation of satisfaction. These speculations were prompted by two striking results in Table
I: the beta weight for social comparison is highest for love life, and
notably low for grades. These results appear to contradict the everyday
observation that social comparison looms larger in academic achievement than in love. Intrigued by this curious pattern, we carried out two
studies to examine whether correlations accurately reflect the relative
importance of interpersonal and intrapersonal comparisons in global
satisfaction.
STUDY I
The first study consisted of a partial replication of the Emmons-Diener
survey, with one new measure: we asked respondents to evaluate the
CAUSES AND HEURISTICS
225
importance of recent changes and of social comparison in their previous ratings of satisfaction. From the set of domains studied by Emmons
and Diener we selected three "public" domains in which we expected
social comparison to be highly accessible (physical attractiveness,
grades, and housing) and two relatively "private" domains in which
information about other is likely to be more ambiguous (friends and
love life). Our hypothesis was that social comparison would be considered more important in the public than in the private domains, while
correlations would show the opposite pattern.
Method
Subjects. The sample consisted of 149 students (95 men, 52 women, 2
unreported) registered at U.C. Berkeley; all but a few were undergraduates with at least one previous year of college. Median age was 21.
Subjects were recruited in a main artery of campus, and paid $1.50 for
completing a 10-minute survey, which also included a set of questions
for use in an unrelated study.
Survey Construction. Except where indicated below, the questionnaire
was patterned after the original Emmons and Diener survey for the five
selected domains (friends, love life, grades, housing, and physical
attractiveness). 2 The first portion of the survey contained satisfaction
and comparison items. The satisfaction question was worded as follows:
"Please rate below how satisfied you are with each area of your life
presently." The seven-point scale ranged from (1) "extremely dissatisfied" to (4) "neutral" to (7) "extremely satisfied." The social comparison
question was: "Compare yourself to the average college student by
placing a number from the scale below next to each item. Although you
may sometimes feel that you don't really know the answer, just make
your best guess. 'Compared to the average college student, I am
currently...'" The scale ranged from (1) "much worse off than they" to
(4) "about the same" to (7) "much better off than they." The change
question was: "This semester, what changes for better or worse have
you experienced in each of the areas? For each area below, indicate the
changes you have recently experienced." The scale ranged from (1)
"much worse recently than before" to (4) "about the same as before" to
226
CRAIG R. FOX AND DANIEL KAHNEMAN
(7) "much better recently than before. ''3 We also followed Emmons and
Diener in asking subjects how high their hopes and aspirations were in
each area, but this item will not be discussed further.
In the next section, subjects were asked to assess the importance of
interpersonal and intrapersonal comparisons in their judgments of
satisfaction: "In deciding how satisfied you are with an area of your life,
they may be several considerations entering into your judgment.
Different kinds of comparisons, for example, may influence your
reported satisfaction to various degrees. Think back to your judgments
of satisfaction that you made at the beginning of this questionnaire -how important do you think each of the following comparisons was in
your judgment of satisfaction?" Importance was rated on a five-point
scale from (1) "completely unimportant" to (5) "very important," with
no labels for intermediate points. The order of questions about the
importance of interpersonal comparisons ('with other college students')
and intrapersonal comparisons ('with your own past') was counterbalanced over subjects, to prevent a systematic bias.
Results and Discussion
Table II lists mean importance ratings for social comparison and for
change, Pearson correlations of these variable with satisfaction and with
each other, and standardized beta weights for the prediction of satisfaction. The pattern of beta weights closely replicates the results of
Emmons and Diener shown in Table I: in every domain, social comparison accounts for more of the variance in satisfaction responses than
does change. The finding that the beta weight for social comparison is
especially high for love life is also replicated. Note that the absolute
magnitudes of the beta weights are not directly comparable to those of
Table I, because Emmons and Diener included several additional
variables as predictors of satisfaction in their regression.
The new results of the experiment concern the importance ratings,
which suggest a different story. Respondents consistently indicated that
they had attached more importance to change than to social comparison in rating satisfaction. The difference was separately significant
beyond the 0.01 level for every domain except physical attractiveness.
The pattern also held for both sexes in separate analyses, although
CAUSES AND HEURISTICS
227
TABLE 1I
Mean importance ratings, standardized beta weights and correlations for five domains
of satisfaction
(G - global satisfaction;S -- social comparison;C -- change)
Importance
Std. fl-weight
C
Correlation
S-G
C-G
Coefficient
S-C
Dom~n
S
C
S
Friends
Love life
Grades
Housing
Attract
2.66
2.58
3.32
2.82
3.09
3.58
3.39
3.92
3.26
3.30
0.45
0.85
0.64
0.49
0.53
0.28
0.25
0.41
0.35
0.19
0.54
0.82
0.59
0.62
0.59
0.29
0.45
0.12
0.54
0.30
0.41
0.53
0.40
0.57
0.32
some significant gender differences were found: social comparison was
more important for women than for men in determining satisfaction
with grades, and recent changes were more important for women than
for men in the domains of physical attractiveness and housing.
The finding that people report change to be more important than
social' comparison could be an artifact of social desirability: it may be
9 embarassing to admit that one's satisfaction with any domain of life is
largely determined by envy or pride. However, the pattern of differences between the rated importance of interpersonal and intrapersonal
comparisons for different domains is not obviously affected by social
desirability. Recall that the domains selected for the study were chosen
to vary in the accessibility of social comparisons: we expected accessibility of social information to be high in the public domains (grades,
housing, and physical attractiveness), and low in the private domains
(friends, and love life). For each subject we computed the difference
between importance ratings of social comparison and of change. These
differences were then averaged, separately for the public and for the
private domains.
The results were consistent with predictions: the mean difference
favoring change was 0.84 for the private domains (love life, friends),
but only 0.42 for the public domains (grades, attractiveness, housing)
(t(145) --- 4.41, p < 0.01). The difference between private and public
domains was equally large for men and for women. Thus, Study I
supports the hypothesis that the correlations between ratings of global
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CRAIG R. FOX AND DANIEL KAHNEMAN
satisfaction and of social comparison do not necessarily reflect the
relative importance of these comparisons.
STUDY II
The judgment model of well-being (Schwarz and Strack, 1991) suggests
that the reference norm to which people compare their state is labile
(see also Kahneman and Miller, 1986). As a consequence, we should
expect evaluations of satisfaction to vary with the momentary salience
of different standards of comparison. For example, Strack and his
colleagues (1990) found that subjects reported a higher satisfaction
with their health after listening to a confederate describe how a severe
medical condition reduced his enjoyment of life. Furthermore, subjects
reported greater general satisfaction with their lives if the confederate
was seated in plain view while they made their ratings.
Responses to survey questions can be strongly influenced by topics
raised earlier in the survey (e.g., Schuman and Presser, 1981). Strack
et al, (1988) reported a striking example. They manipulated the order
of two questions in a survey of American college students: how often
they go out on dates, and how happy they are with their lives. The two
measures were uncorrelated when the happiness question was asked
first (r = 0.12), but the correlation was dramatically higher (r -- 0.66)
when the happiness question immediately followed the dating question.
Evidently, the salience of dating in the evaluation of overall happiness
can be greatly increased by raising this topic just before the more global
question. The effect is not symmetric, of course, because it is always
natural for respondents to answer the dating question by consulting
their memory, rather than by considering their general happiness.
The findings of Strack et aL (1988) suggested an additional test of
the main hypothesis of this article. We proposed earlier that social
comparisons in private domains of life (e.g., love or friendship) are
sometimes inferred from (or anchored on) global satisfaction. This
heuristic is most likely to be used, we assume, when the salience of
global satisfaction is high. Salience can be enhanced, for example, by
asking subjects to evaluate satisfaction just before they evaluate social
comparison. Thus, we expect an order effect on the correlation between
global satisfaction and social comparison, but only in private domains
CAUSES AND HEURISTICS
229
where direct cues for social comparison are lacking. This analysis
assumes that global satisfaction can be used to evaluate social comparison, and it also assumes that this heuristic is optional. The order
effect arises because the request to make a social comparison does not
inevitably evoke the heuristic of consulting global satisfaction.
Questions about satisfaction preceded questions about social comparison and about recent changes in the Emmons-Diener study, as they
did in our Study I. This sequence is appropriate if the goal is to avoid
suggesting to subjects that they use particular constituent judgments in
evaluating the global questions. However, if there is a possibility that
the specific judgments are affected by the global ones, or by one
another, then order must be varied. We therefore conducted a survey
using six different forms, representing the six possible orderings of the
sections dealing with satisfaction, social comparison, and recent change.
The main purpose of the experiment was to test the specific hypothesis
that, in private domains, social comparisons are inferred from global
satisfaction. If this dependence is asymmetric then the correlation will
be higher, in these domains, when global satisfaction is rated before
social comparison rather than after it. The design also permitted other
possible order effects to be explored.
Method
Subjects. The sample consisted of 125 undergraduates (63 men, 60
women, 2 unreported) registered in an introductory psychology class at
San Jose State University. Median age was 19. Subjects received course
credit for completing a packet of questionnaires which included a wellbeing survey.
Survey construction. At the beginning of the questionnaire, subjects
were given a preview of the items to be asked: "In the next couple of
pages, we would like you to evaluate five areas of your life: your grades,
your housing arrangements, your physical attractiveness, your friends,
and your love life. We want to know how satisfied you are in each area,
how you feel you compare with others, and what kinds of changes you
have experienced recently. Your responses are completely anonymous".
Following the instructions, subjects were asked to make five evaluations
230
CRAIG R. FOX AND DANIEL KAHNEMAN
(one for each domain) for each judgment type (satisfaction, social
comparison, recent change). Each judgment type had instructions
matching those in Study I, with minor variations of wording. Six survey
forms were used, representing all possible orders of the ratings of
global satisfaction, social comparison, and change.
Results and Discussion
The purpose of this study was to examine the effects of variations of
order on the correlations between ratings of global satisfaction, social
comparison and intrapersonal change, for each of the five life domains.
We therefore computed two correlations for each pair of measures,
grouping together the three forms for which the order of these measures was the same. The pairs of correlations are shown in Table III,
along with a test of statistical significance for the difference between
the correlations (normal test, after transformation of coefficients to
Fisher's z).
Our hypothesis specifically predicted a substantial order effect for
only two of the fifteen comparisons included in Table III: the correlations between global satisfaction and social comparison for the two
private domains (love life and friends). In both these cases we expected
the correlation to be higher when satisfaction was assessed first. The
TABLE HI
Correlation of items within domains as a function of question order
(G -- global satisfaction; S -- social comparison; C -- change)
Question order
Domain
Grades
Attractiveness
Housmg
Friends
Lovelife
N
a 0.05 < p < 0.10
b p < 0.01
S-G
G-S
C-G
G-C
S-C
C-S
0.614
0.690 a
0.755 a
0.408 b
0.555 b
0.600
0.530
0.580
0.760
0.868
0.566
0.505
0.575
0.538
0.620
0.386
0.577
0.664
0.473
0.623
0.380
0.608
0.671
0.576
0.440 a
0.422
0.436
0.538
0.509
0.669
62
59
60
61
62
63
CAUSES AND HEURISTICS
231
results are striking: the two correlations for which a difference was
predicted are the only ones for which the difference is significant (p <
0.01). These results confirm the idea that global satisfaction provides an
optional (not obligatory) heuristic for social comparisons.
Three other differences in Table I approach significance (0.05 <
p < 0.10). For love life (but not for friendships) there is an indication
of an order effect on the correlation between change and social
comparison; the direction of the asymmetry suggests that change may
also be used as a heuristic to evaluate social standing. For two of the
three public domains, the correlation between social comparison and
satisfaction is higher when social comparison is queried first than when
it is queried second. Applying the argument that we have borrowed
from Strack et al. (1988), this result suggests that social comparison is
an optional determinant of global satisfaction in public domains, and
that its weight is increased by a favorable ordering of questions.
The study of order effects provides a useful diagnostic tool for the
analysis of relations between judgments of different variables. By this
diagnostic, reliance on global satisfaction has been identified as an
optional heuristic for the judgment of social comparison in private
domains, and social comparison may be an optional heuristic for
judgments of global satisfaction in some public domains. One salient
exception is the domain of grades, where the social comparison may be
so natural that it is an obligatory heuristic. The evaluation of recent
changes in life domains shows no order effects, implying that these
assessments are probably made without specifically consulting either
global satisfaction or social comparison.
GENERAL DISCUSSION
The results of both studies illustrate the power of a judgmental analysis
of measures of well-being, as well as the pitfalls of drawing causal
inferences from correlations between these measures. In Study I we
found that the subjective importance that respondents assign to social
comparison is relatively low in private life domains, whereas the
correlation between social comparison and global satisfaction in these
domains is notably high. Global satisfaction was assessed before social
comparison in Study I. Study II showed that reversing the order of the
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questions significantly reduces the correlation between these ratings,
presumably by curtailing the use of global satisfaction as a heuristic for
judging social comparison. The results are embarrassing for any view
that treats the rating of well-being as a read-out from a well-defined
subjective dimension onto a response scale. The alternative view is that
assessing one's well-being is a complex task, which subjects solve in
part by opportunistic reliance on cues provided by the question itself,
by earlier questions in the survey, and by the circumstances of the
moment (Schwarz and Strack, 1991).
The question of what are the "determinants" of happiness or of any
particular aspect of well-being does not become meaningless in the
context of a judgmental analysis. The substantive conclusion of our
judgmental analysis is that Emmons and Diener probably overestimated
the importance of social comparison in determining satisfaction in
private domains, not that the question they posed was pointless. Like
physical or mental health, intelligence, beauty, and good character,
happiness is a complex multidimensional object of judgment. Thus, the
individual's present state and past history, and the relation of these with
the circumstances of relevant others are all potential determinants of
satisfaction with life domains. Furthermore, the very meaning of
"happiness" to a subject can change depending on the circumstances of
the moment. The causal analysis of labile, error-prone and interdependent judgments presents a difficult problem of how to disentangle the
factors that affect the object of judgment from the factors that affect the
judgment itself. We do not believe that these difficulties make the
enterprise of analyzing well-being impossible. However, it now appears
that the conceptual basis for this analysis should be broadened to
include relevant findings of cognitive psychology, and that the standard
correlational techniques of the field should in some cases be supplemented by an experimental approach.
NOTES
* University of California at Berkeley. The first study is based on an honors thesis
submitted by Craig Fox to the Department of Psychology at the University of
California. The research was partly supported by a grant from the Sloan Foundation
and by the Air Force Office of Scientific Research under grant number AFOSR 888206 to Daniel Kahneman. We thank Amy Hayes for her assistance in data collection.
CAUSES AND H E U R I S T I C S
233
1 Some of the comments that follow raise questions about the method used by
Emmons and Diener. It is fair to relate that, before learning of their work, we planned a
study using precisely the method that we now question. We were drawn to a critical
scrutiny by the surprising results that this common method yielded in their research.
2 We are grateful to E. Diener and R. A. Emmons for providing us a copy of their
survey instrument.
3 The last two words were added to the question used by Emmons and Diener, to
eliminate a possible ambiguity.
REFERENCES
Argyle, M.: 1987, The Psychology of Happiness (Methuen, New Work).
Brickman, P. and Campbell, D. T.: 1971, 'Hedonic relativism and planning the good
society', in M. H. Appley (ed) Adaptation-Level Theory: A Symposium (Academic
Press, New York).
Crosby, F.: 1982, Relative Deprivation and Working Women (Oxford University Press,
New York).
Diener, E.: 1989, 'Issues in defining subjective well-being and ill-being', unpublished
manuscript (University of Illinois, Urbana-Champaign).
Diener, E.: 1984, 'Subjective well-being', Psychological Bulletin 95,542--575.
Emmons, R. A. and Diener, E.: 1985, 'Factors predicting satisfaction judgments: A
comparative examination', Social Indicators Research 16, 157-- 167.
Festinger, L.: 1954, 'A theory of social comparison process', Human Relations 7, 230-243.
Helson, H.: 1964, Adaptation Level Theory: An Experimental and Systematic Approach to Behavior (Harper & Row, New York).
Hippler, H. J., Schwarz, N., and Sudman, S. (eds): 1987, Social Information Processing
and Survey Methodology (Springer-Verlag, New York).
Kahneman, D. and Miller, D.: 1986, 'Norm theory: Comparing reality to its alternatives', Psychological Review 93, 136-- 153.
Schuman, H. and Presser, S.: 1981, Questions and Answers in Attitude Surveys:
Experiments on Question Form, Wording and Context (Academic Press, New
York).
Schwarz, N. and Clore, G.: 1983, 'Mood, misattribution, and judgments of well-being:
Informative and directive functions of affective states', Journal of Personality and
Social Psychology 45, 513--523.
Schwarz, N. and Strack, F.: 1991, 'Evaluating one's life: A judgment model of wellbeing', in F. Strack, M. Argyle, and N. Schwarz (eds) Subjective Well-Being
(Pergamon Press, Oxford).
Smith, R. H., Diener, E., and Wedell, D. H.: 1989, 'Intrapersonal and social comparison
determinants of happiness: A range-frequency analysis', Journal of Personality and
Social Psychology 56, 317--325.
Strack, F., Martin, L. L., and Schwarz, N.: 1988, 'Priming and Communication: Social
determinants of information use in judgments of life satisfaction', European Journal
of Social Psychology 18, 429--442.
Strack, F., Schwarz, N., Chassein, B., Kern, D., and Wagner, D.: 1990, 'Salience of
comparison standards and the activation of social norms: Consequences for judgments of happiness and their communication', British Journal of Social Psychology
29(4), 303--314.
Tourangeau, R.: 1984, 'Cognitive science and survey methods', in T. B. Jabine, M. L.
Straf, J. M. Tanur, and R. Tourangeau (eds) Cognitive Aspects of Survey Methodol-
234
C R A I G R. F O X A N D D A N I E L K A H N E M A N
ogy: Building a Bridge Between Disciplines (National Academy Press, Washington
D.C.).
van de Stadt, H., Kapteyn, A., and van de Geer, S.: 1985, 'The relativity of utility:
Evidence from panel data', The review of Economics and Statistics 67, 179--187.
Dept. of Psychology,
University of California,
Berkeley, CA 94720, U.S.A.